We need volatilty based trading instruments , the more the better. WHY?

Well, if one thinks of options written, all the delta hedges based on Blackscholes break down if the volatility is a stochastic process. If Vol is a function of spot and time, it is fine, but most of the cases , one cannot assume that. So, if delta hedge of Black Scholes world is useless, what can one do ? Look for volatility based trading instruments like VIX and then delta hedge it.

More over, one also needs to think of the correlation between the stocks and vol for it plays a significant role in the pricing of derivatives. Correlation modeling is notoriously difficult . May be one must look at Garch type mean reverting process to value options..However , that doesn’t solve the problem. How do you delta hedge it ?

So , there you are : In the world of stochastic volatility you have 3 issues :**Pricing ,Model ,Calibration and Hedging
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Let’s take an example to understand the problem better . Lets consider american barrier with stochastic volatility . Simple Binomial trees are useless for they cannot capture stochastic volatility. MonteCarlo is slow and will suck. Finite Difference, naa…Getting a closed form using Girsanov , I doubt it, haven’t tried though . How do you price it ? How do you calibrate it ? and most importantly , How do you hedge it ?After 12 months of studying math-fin, I have some clue on pricing and calibration but ABSOLUTELY no clue on hedging such an option :( . Long way to go!!